Problem 59 - Algebra A Combined Function

Question

Evaluate each expression when \(x=-5, y=4,\) and \(t=10\). \(x-y\)

Step-by-Step Solution

Answer

The value of the expression is \(-9\).

Step 1: Identify the variables

The expression we are asked to evaluate is \(x-y\). We need to identify the variables within this expression: \(x\) and \(y\).

Step 2: Substitute the values

Replace \(x\) with \(-5\) and \(y\) with \(4\) in the expression. This gives us: \(-5 - 4\).

Step 3: Perform the subtraction

Subtract \(4\) from \(-5\). The expression \(-5 - 4 \) yields \(-5 - 4 = -9\).

Key Concepts

Evaluating Expressions

Evaluating expressions is a fundamental skill in algebra. When you evaluate an expression, you are finding out what it equals when the variables have specific values. Consider an algebraic expression like \(x-y\). To evaluate it, you'll need to replace each variable with its given value and perform the arithmetic operations indicated. This helps you see what the algebraic expression represents numerically.

• Identify the expression: Look at the algebraic expression that needs to be evaluated.
• Substitute each variable with the given number.
• Perform the arithmetic operations to arrive at the final numerical answer. This shows the result of replacing the variables with specific numbers.

Through practice, evaluating expressions becomes a quicker and more intuitive process. It's a critical step in solving more complex algebraic problems as well.

Variable Substitution

Variable substitution involves replacing variables with specific values. This is key for calculating actual values in expressions. In our example \(x-y\), the variables are \(x\) and \(y\). You are given values such as \(x=-5\) and \(y=4\).

• Make sure you clearly understand which values correspond to which variables.
• Carefully substitute each variable in the expression with its given value.
• Rewrite the expression with these numbers to see it in a form that is ready for mathematical operations.

After substituting, the expression will no longer contain variables but rather simple numbers, making it easy to calculate the result.

Arithmetic Operations

Arithmetic operations are the basic calculations you perform after substituting variables. They include addition, subtraction, multiplication, and division. In our specific example of \(x-y\), after substitution, we are left with the task of performing subtraction.

Subtraction takes place when you need to calculate the difference between two numbers. After substituting \(x=-5\) and \(y=4\), the expression becomes \(-5 - 4\), which equates to \(-9\). This operation helps transform an algebraic expression into a definite numeric result.

• Perform any operation as indicated by the expression. For subtraction, count back from the first number by the second number.
• Understand that the sign of the result is based on the starting point and how much is subtracted.

Mastering arithmetic operations is fundamental for tackling more complex problems as it enables you to reliably compute results from algebraic expressions.